Geodesic
BIEMBEDDINGS OF LATIN SQUARES AND HAMILTONIAN DECOMPOSITIONS
Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 443-457

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DOI

Face 2-colourable triangulations of complete tripartite graphs $K_{n,n,n}$ correspond to biembeddings of Latin squares. Up to isomorphism, we give all such embeddings for $n=3,4,5$ and 6, and we summarize the corresponding results for $n=7$. Closely related to these are Hamiltonian decompositions of complete bipartite directed graphs $K^*_{n,n}$, and we also give computational results for these in the cases $n=3,4,5$ and 6.
DOI : 10.1017/S0017089504001922
Mots-clés : 05B15, 05C10 
GRANNELL, M. J.; GRIGGS, T. S.; KNOR, M. BIEMBEDDINGS OF LATIN SQUARES AND HAMILTONIAN DECOMPOSITIONS. Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 443-457. doi: 10.1017/S0017089504001922
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     author = {GRANNELL, M. J. and GRIGGS, T. S. and KNOR, M.},
     title = {BIEMBEDDINGS {OF} {LATIN} {SQUARES} {AND} {HAMILTONIAN} {DECOMPOSITIONS}},
     journal = {Glasgow mathematical journal},
     pages = {443--457},
     year = {2004},
     volume = {46},
     number = {3},
     doi = {10.1017/S0017089504001922},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504001922/}
}
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